import {Curve, Vector3} from '../../three.module.js';

/**
 * A bunch of parametric curves
 *
 * Formulas collected from various sources
 * http://mathworld.wolfram.com/HeartCurve.html
 * http://en.wikipedia.org/wiki/Viviani%27s_curve
 * http://www.mi.sanu.ac.rs/vismath/taylorapril2011/Taylor.pdf
 * https://prideout.net/blog/old/blog/index.html@p=44.html
 */

// GrannyKnot

class GrannyKnot extends Curve {

  getPoint(t, optionalTarget = new Vector3()) {

    const point = optionalTarget;

    t = 2 * Math.PI * t;

    const x = -0.22 * Math.cos(t) - 1.28 * Math.sin(t) - 0.44 * Math.cos(3 * t) - 0.78 * Math.sin(3 * t);
    const y = -0.1 * Math.cos(2 * t) - 0.27 * Math.sin(2 * t) + 0.38 * Math.cos(4 * t) + 0.46 * Math.sin(4 * t);
    const z = 0.7 * Math.cos(3 * t) - 0.4 * Math.sin(3 * t);

    return point.set(x, y, z).multiplyScalar(20);

  }

}

// HeartCurve

class HeartCurve extends Curve {

  constructor(scale = 5) {

    super();

    this.scale = scale;

  }

  getPoint(t, optionalTarget = new Vector3()) {

    const point = optionalTarget;

    t *= 2 * Math.PI;

    const x = 16 * Math.pow(Math.sin(t), 3);
    const y = 13 * Math.cos(t) - 5 * Math.cos(2 * t) - 2 * Math.cos(3 * t) - Math.cos(4 * t);
    const z = 0;

    return point.set(x, y, z).multiplyScalar(this.scale);

  }

}

// Viviani's Curve

class VivianiCurve extends Curve {

  constructor(scale = 70) {

    super();

    this.scale = scale;

  }

  getPoint(t, optionalTarget = new Vector3()) {

    const point = optionalTarget;

    t = t * 4 * Math.PI; // normalized to 0..1
    const a = this.scale / 2;

    const x = a * (1 + Math.cos(t));
    const y = a * Math.sin(t);
    const z = 2 * a * Math.sin(t / 2);

    return point.set(x, y, z);

  }

}

// KnotCurve

class KnotCurve extends Curve {

  getPoint(t, optionalTarget = new Vector3()) {

    const point = optionalTarget;

    t *= 2 * Math.PI;

    const R = 10;
    const s = 50;

    const x = s * Math.sin(t);
    const y = Math.cos(t) * (R + s * Math.cos(t));
    const z = Math.sin(t) * (R + s * Math.cos(t));

    return point.set(x, y, z);

  }

}


// HelixCurve

class HelixCurve extends Curve {

  getPoint(t, optionalTarget = new Vector3()) {

    const point = optionalTarget;

    const a = 30; // radius
    const b = 150; // height

    const t2 = 2 * Math.PI * t * b / 30;

    const x = Math.cos(t2) * a;
    const y = Math.sin(t2) * a;
    const z = b * t;

    return point.set(x, y, z);

  }

}

// TrefoilKnot

class TrefoilKnot extends Curve {

  constructor(scale = 10) {

    super();

    this.scale = scale;

  }

  getPoint(t, optionalTarget = new Vector3()) {

    const point = optionalTarget;

    t *= Math.PI * 2;

    const x = (2 + Math.cos(3 * t)) * Math.cos(2 * t);
    const y = (2 + Math.cos(3 * t)) * Math.sin(2 * t);
    const z = Math.sin(3 * t);

    return point.set(x, y, z).multiplyScalar(this.scale);

  }

}

// TorusKnot

class TorusKnot extends Curve {

  constructor(scale = 10) {

    super();

    this.scale = scale;

  }

  getPoint(t, optionalTarget = new Vector3()) {

    const point = optionalTarget;

    const p = 3;
    const q = 4;

    t *= Math.PI * 2;

    const x = (2 + Math.cos(q * t)) * Math.cos(p * t);
    const y = (2 + Math.cos(q * t)) * Math.sin(p * t);
    const z = Math.sin(q * t);

    return point.set(x, y, z).multiplyScalar(this.scale);

  }

}

// CinquefoilKnot

class CinquefoilKnot extends Curve {

  constructor(scale = 10) {

    super();

    this.scale = scale;

  }

  getPoint(t, optionalTarget = new Vector3()) {

    const point = optionalTarget;

    const p = 2;
    const q = 5;

    t *= Math.PI * 2;

    const x = (2 + Math.cos(q * t)) * Math.cos(p * t);
    const y = (2 + Math.cos(q * t)) * Math.sin(p * t);
    const z = Math.sin(q * t);

    return point.set(x, y, z).multiplyScalar(this.scale);

  }

}


// TrefoilPolynomialKnot

class TrefoilPolynomialKnot extends Curve {

  constructor(scale = 10) {

    super();

    this.scale = scale;

  }

  getPoint(t, optionalTarget = new Vector3()) {

    const point = optionalTarget;

    t = t * 4 - 2;

    const x = Math.pow(t, 3) - 3 * t;
    const y = Math.pow(t, 4) - 4 * t * t;
    const z = 1 / 5 * Math.pow(t, 5) - 2 * t;

    return point.set(x, y, z).multiplyScalar(this.scale);

  }

}

function scaleTo(x, y, t) {

  const r = y - x;
  return t * r + x;

}

// FigureEightPolynomialKnot

class FigureEightPolynomialKnot extends Curve {

  constructor(scale = 1) {

    super();

    this.scale = scale;

  }

  getPoint(t, optionalTarget = new Vector3()) {

    const point = optionalTarget;

    t = scaleTo(-4, 4, t);

    const x = 2 / 5 * t * (t * t - 7) * (t * t - 10);
    const y = Math.pow(t, 4) - 13 * t * t;
    const z = 1 / 10 * t * (t * t - 4) * (t * t - 9) * (t * t - 12);

    return point.set(x, y, z).multiplyScalar(this.scale);

  }

}

// DecoratedTorusKnot4a

class DecoratedTorusKnot4a extends Curve {

  constructor(scale = 40) {

    super();

    this.scale = scale;

  }

  getPoint(t, optionalTarget = new Vector3()) {

    const point = optionalTarget;

    t *= Math.PI * 2;

    const x = Math.cos(2 * t) * (1 + 0.6 * (Math.cos(5 * t) + 0.75 * Math.cos(10 * t)));
    const y = Math.sin(2 * t) * (1 + 0.6 * (Math.cos(5 * t) + 0.75 * Math.cos(10 * t)));
    const z = 0.35 * Math.sin(5 * t);

    return point.set(x, y, z).multiplyScalar(this.scale);

  }

}

// DecoratedTorusKnot4b

class DecoratedTorusKnot4b extends Curve {

  constructor(scale = 40) {

    super();

    this.scale = scale;

  }

  getPoint(t, optionalTarget = new Vector3()) {

    const point = optionalTarget;

    const fi = t * Math.PI * 2;

    const x = Math.cos(2 * fi) * (1 + 0.45 * Math.cos(3 * fi) + 0.4 * Math.cos(9 * fi));
    const y = Math.sin(2 * fi) * (1 + 0.45 * Math.cos(3 * fi) + 0.4 * Math.cos(9 * fi));
    const z = 0.2 * Math.sin(9 * fi);

    return point.set(x, y, z).multiplyScalar(this.scale);

  }

}


// DecoratedTorusKnot5a

class DecoratedTorusKnot5a extends Curve {

  constructor(scale = 40) {

    super();

    this.scale = scale;

  }

  getPoint(t, optionalTarget = new Vector3()) {

    const point = optionalTarget;

    const fi = t * Math.PI * 2;

    const x = Math.cos(3 * fi) * (1 + 0.3 * Math.cos(5 * fi) + 0.5 * Math.cos(10 * fi));
    const y = Math.sin(3 * fi) * (1 + 0.3 * Math.cos(5 * fi) + 0.5 * Math.cos(10 * fi));
    const z = 0.2 * Math.sin(20 * fi);

    return point.set(x, y, z).multiplyScalar(this.scale);

  }

}

// DecoratedTorusKnot5c

class DecoratedTorusKnot5c extends Curve {

  constructor(scale = 40) {

    super();

    this.scale = scale;

  }

  getPoint(t, optionalTarget = new Vector3()) {

    const point = optionalTarget;

    const fi = t * Math.PI * 2;

    const x = Math.cos(4 * fi) * (1 + 0.5 * (Math.cos(5 * fi) + 0.4 * Math.cos(20 * fi)));
    const y = Math.sin(4 * fi) * (1 + 0.5 * (Math.cos(5 * fi) + 0.4 * Math.cos(20 * fi)));
    const z = 0.35 * Math.sin(15 * fi);

    return point.set(x, y, z).multiplyScalar(this.scale);

  }

}

const Curves = {
  GrannyKnot: GrannyKnot,
  HeartCurve: HeartCurve,
  VivianiCurve: VivianiCurve,
  KnotCurve: KnotCurve,
  HelixCurve: HelixCurve,
  TrefoilKnot: TrefoilKnot,
  TorusKnot: TorusKnot,
  CinquefoilKnot: CinquefoilKnot,
  TrefoilPolynomialKnot: TrefoilPolynomialKnot,
  FigureEightPolynomialKnot: FigureEightPolynomialKnot,
  DecoratedTorusKnot4a: DecoratedTorusKnot4a,
  DecoratedTorusKnot4b: DecoratedTorusKnot4b,
  DecoratedTorusKnot5a: DecoratedTorusKnot5a,
  DecoratedTorusKnot5c: DecoratedTorusKnot5c
};

export {Curves};
